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C2×D6235 #38735566

order24940
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD12470
direct productC2×D6235
unambiguous semidirect product(C2×C5)⋊D1247
unambiguous semidirect product(C2×C29)⋊D215
unambiguous semidirect product(C2×C43)⋊D145

Splittings

Fitting, socleC2×C5×C29×C43 ⋊ C2
derived, HallC5×C29×C43 ⋊ C22
HallC29×C43 ⋊ C2×D5
HallC5×C43 ⋊ C2×D29
HallC5×C29 ⋊ C2×D43
SylowC43 ⋊ C2×D145
SylowC29 ⋊ C2×D215
SylowC5 ⋊ C2×D1247

Subgroups

subgroupG/H
center, hypercenterC2D6235
commutator, cosocle, hypocenterC5×C29×C43C22
FrattiniC1G
Fitting, socleC2×C5×C29×C43C2
LCSG ▷ C5×C29×C43
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 79
transitive degreeμt(G) = 12470

A minimal faithful permutation representation — 2 generators on 79 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79);(4,7)(5,6)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,79)(39,78)(40,77)(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)(53,64)(54,63)(55,62)(56,61)(57,60)(58,59)

Conjugacy classes & character table

6238 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD24940
maximal normal subgroup ofD24940
maximal quotient ofDic12470, D24940

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24940, 35);